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Let X1, ..., Xn be a random sample from the lognormal distribution, Lognormal(#, 1), whose pdf is: f(x | 4, A ) = 1 exp (In x - p) rV2xX r > 0. (a) Show that the MLE of u and A are A = 1 27, In X, and A = 1 ER, (In Xi - A)2. (b) It is known that In Xi ~ N(A, A). i. Derive the standard deviation of 1. ii. Derive a 100 . (1 - o)% confidence interval for 1. (c) (R) Consider the following dataset: 12.9 2.3 2.4 65.0 6.7 1.8 1.5 1.7 248.7 1. 0 2.0 4.9 3.6 4. 1 6.8 i. Calculate the standard error of 1. ii. Assuming a lognormal distribution is an appropriate model for these data, com- pute the maximum likelihood estimate of A and give a 95% CI